Mesh refinement processes based on the generalized bisection of simplices. (English) Zbl 0574.65133

Rivara, Maria-Cecilia

SIAM J. Numer. Anal. 21, 604-613 (1984).

Mesh-refinement processes based on the generalized bisection of simplices are discussed and characterized in the context of the general theory of W. C. Rheinboldt [ibid. 17, 766-778 (1980; Zbl 0472.65009)]. Then it is proved that such processes allow the construction of sequences of naturally smooth conforming and nested nonuniform meshes. In fact it is shown that there exists a generalized mesh-refinement operator that for any conforming triangulation \(\Delta\) and for any \(V\subset \Delta\), produces a nested, smooth, conforming triangulation \(\Delta^*\) containing successors of all elements of V and such that the minimum cell-size of \(\Delta^*\) is bounded from below by half the minimum cell- size of \(\Delta\). Two conforming mesh-refinement algorithms that allow the selective refinement of computational triangulations are explicitly given.

MSC:

65N50

Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs

Keywords:

Mesh-refinement; bisection of simplices; smooth conforming and nested nonuniform meshes; selective refinement; computational triangulations